Species distribution models (SDMs) are widely used to relate species occurrence and density to local environmental conditions, and often include a spatially correlated variable to account for spatial patterns in residuals. Ecologists have extended SDMs to include spatially varying coefficients (SVCs), where the response to a given covariate varies smoothly over space and time. However, SVCs see relatively little use perhaps because they remain less known relative to other SDM techniques. We therefore review ecological contexts where SVCs can improve the interpretability and descriptive power from SDMs, including local responses to regional indices that represent ecological teleconnections; density-dependent habitat selection; spatially varying detectability; and context-dependent covariate responses that represent interactions with unmeasured covariates. We then illustrate three additional examples in detail using the vector autoregressive spatio-temporal (VAST) model. First, a spatially varying decadal trends model identifies decadal trends for arrowtooth flounder Atheresthes stomias density in the Bering Sea from 1982 to 2019. Second, a trait-based joint SDM highlights the role of body size and temperature in spatial community assembly in the Gulf of Alaska. Third, an age-structured SDM for walleye pollock Gadus chalcogrammus in the Bering Sea contrasts cohorts with broad spatial distributions (1996 and 2009) and those that are more spatially constrained (2002 and 2015). We conclude that SVCs extend SDMs to address a wide variety of ecological contexts and can be used to better understand a range of ecological processes, e.g. density dependence, community assembly and population dynamics.

中文翻译：

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空间变化系数可以提高物种分布模型的简约性和描述性

物种分布模型 (SDM) 广泛用于将物种发生和密度与当地环境条件相关联，并且通常包括空间相关变量以解释残差中的空间模式。生态学家已将 SDM 扩展到包括空间变化系数 (SVC)，其中对给定协变量的响应随空间和时间平滑变化。然而，SVC 的使用相对较少，这可能是因为它们相对于其他 SDM 技术而言仍然鲜为人知。因此，我们回顾了 SVC 可以提高 SDM 的可解释性和描述能力的生态环境，包括当地对代表生态遥相关的区域指数的反应；依赖于密度的栖息地选择；空间变化的可探测性；和上下文相关的协变量响应，表示与未测量的协变量的交互。然后，我们使用向量自回归时空 (VAST) 模型详细说明了另外三个示例。首先，空间变化的年代际趋势模型确定了箭齿比目鱼的年代际趋势1982 年至 2019 年白令海中的Atheresthes stomias密度。其次，基于特征的联合 SDM 强调了体型和温度在阿拉斯加湾空间群落组装中的作用。第三，白令海中角膜狭鳕Gadus chalcogrammus的年龄结构 SDM 对比了具有广泛空间分布的队列（1996 年和 2009 年）和空间分布更受限的队列（2002 年和 2015 年）。我们得出结论，SVC 扩展了 SDM 以解决各种生态环境，并可用于更好地理解一系列生态过程，例如密度依赖性、社区集会和种群动态。